Why are my Verticies/Edges/Faces locked from moving up and down?
The scale of the object in "object mode" is set to 0. While scaling the z-axis with 0 in edit mode is great to get a flat surface, in object mode, this leads to this expected but explainable behavior.



Set the scale in z-direction to 1 while in object mode and it will work again. 

On another note I would be VERY CAREFUL to have an object SCALED IN OBJECT MODE, if you are trying to model a real world floor plan with REAL WORLD UNITS. 

I never use scale/rotation in object mode unless I'm compositing multiple objects together.

In this case I would suggest to apply apply scale in object mode and then select all and scale in edit mode.